Self-organized Patterns Research Articles

Mesoscale heterogeneity is a critical determinant for spiral pattern formation in developing social amoeba

Heterogeneity is a critical determinant for multicellular pattern formation. Although the importance of microscale and macroscale heterogeneity at the single-cell and whole-system levels, respectively, has been well accepted, the presence and functions of mesoscale heterogeneity, such as cell clusters with distinct properties, have been poorly recognized. We investigated the biological importance of mesoscale heterogeneity in signal-relaying abilities (excitability) in the self-organization of spiral waves of intercellular communications by studying the self-organized pattern formation in a population of Dictyostelium discoideum cells, a classical signal-relaying system model. By utilizing pulse-count analysis to evaluate cellular excitability, we successfully visualized the development of mesoscale heterogeneity in excitability, whose spatial scale was comparably large to that of the traveling waves of intercellular communication. Together with perturbation experiments, our detailed analysis of the structural change in mesoscale heterogeneity and associated wave dynamics demonstrated the functional importance of mesoscale heterogeneity in generating the spiral wave pattern, whose experimental observations were first realized. We propose that mesoscale heterogeneity, in addition to microscale and macroscale heterogeneities, is a critical determinant of diverse multicellular pattern formations.

Pattern formations and their active manipulation in a Rydberg noisy-dressed Bose-Einstein condensate.

We investigate the formation and manipulation of spatial patterns and their structural phase transitions by examining the effects of laser linewidth on the dynamics of Rydberg noise-dressed Bose-Einstein condensates (RnD BECs). We discover that the homogeneous matter wave can transition into various types of self-organized patterns, which are manipulated by tuning the laser linewidth, control field intensity, and atomic density. Remarkably, the system exhibits stable nonlocal matter-wave solitons, vortices, and soliton molecules under specific laser linewidths.

Self-Organized Patterns in Non-Reciprocal Active Droplet Systems.

Non-equilibrium patterns are widespread in nature and often arise from the self-organization of constituents through nonreciprocal chemotactic interactions. In this study, we demonstrate how active oil-in-water droplet mixtures with predator-prey interactions can result in a variety of self-organized patterns. By manipulating physical parameters, the droplet diameter ratio and number ratio, we identify distinct classes of patterns within a binary droplet system, rationalize the pattern formation, and quantify motilities. Experimental results are recapitulated in numerical simulations using a minimal computational model that solely incorporates chemotactic interactions and steric repulsion among the constituents. The time evolution of the patterns is investigated and chemically explained. We also investigate how patterns vary with differing interaction strength by altering surfactant composition. Leveraging insights from the binary droplet system, the framework is extended to a ternary droplet mixture composed of multiple chasing droplet pairs to create chemically directed hierarchical organization. Our findings demonstrate how rationalizable, self-organized patterns can be programmed in a chemically minimal system and provide the basis for exploration of emergent organization and higher order complexity in active colloids.

Self-organized pattern formation in the developing mouse neural tube by a temporal relay of BMP signaling.

Developing tissues interpret dynamic changes in morphogen activity to generate cell type diversity. To quantitatively study bone morphogenetic protein (BMP) signaling dynamics in the mouse neural tube, we developed an embryonic stem cell differentiation system tailored for growing tissues. Differentiating cells form striking self-organized patterns of dorsal neural tube cell types driven by sequential phases of BMP signaling that are observed both invitro and invivo. Data-driven biophysical modeling showed that these dynamics result from coupling fast negative feedback with slow positive regulation of signaling by the specification of an endogenous BMP source. Thus, in contrast to relays that propagate morphogen signaling in space, we identify a BMP signaling relay that operates in time. This mechanism allows for a rapid initial concentration-sensitive response that is robustly terminated, thereby regulating balanced sequential cell type generation. Our study provides an experimental and theoretical framework to understand how signaling dynamics are exploited in developing tissues.

Correlation between temperature distribution and changes in self-organized luminous pattern in an atmospheric pressure DC glow discharge with sheath gas flow

Abstract The self-organized luminous patterns observed above the anode surface in atmospheric-pressure DC glow discharges were changed by the composition of the gas flow. The patterns were observed not only with liquid anodes but also with metal anodes. Various pattern structures were observed by changing the helium gas flow rate in the core and the ambient oxygen gas flow rate supplied during the discharge. When the pattern formation was observed, the emission spectra and the radial spread of the positive column changed, and the voltage–current characteristic also changed. These results suggest that not only the anode surface but the entire discharge affects the pattern formation. Comparing the results for the liquid and metal anodes, the trends in the pattern formation and voltage–current characteristics were almost identical. The gas temperature in the discharge was also investigated in two different ways, by the laser-induced fluorescence spectroscopy of OH radicals and by Rayleigh scattering, showing in good agreement between both methods. Under the condition where the pattern formed, the gas temperature in the discharge was approximately 2500–3000 K and higher than that of the discharge without the pattern formation. Focusing on the gradient of the temperature distribution, the discharge with the pattern formation had a steeper gradient than that of the discharge without the pattern formation. It is suggested that not only the high temperature of the discharge but also the large gradient of the temperature change plays an important role in the pattern formation. The role of oxygen gas in the pattern formation may be the effect of increasing the temperature and altering the temperature gradient in the discharge rather than generating negative ions in the discharge.

Dynamic IoT deployment reconfiguration: A global-level self-organisation approach

The edge–cloud continuum provides a heterogeneous, multi-scale, and dynamic infrastructure supporting complex deployment profiles and trade-offs for application scenarios like those found in the Internet of Things and large-scale cyber–physical systems domains. To exploit the continuum, applications should be designed in a way that promotes flexibility and reconfigurability, and proper management (sub-)systems should take care of reconfiguring them in response to changes in the environment or non-functional requirements. Approaches may leverage optimisation-based or heuristic-based policies, and decision making may be centralised or distributed: this work investigates decentralised heuristic-based approaches. In particular, we focus on the pulverisation approach, whereby a distributed software system is automatically partitioned (“pulverised”) into different deployment units. In this context, we address two main research problems: how to support the runtime reconfiguration of pulverised systems, and how to specify decentralised reconfiguring policies by a global perspective. To address the first problem, we design and implement a middleware for pulverised systems separating infrastructural and application concerns. To address the second problem, we leverage aggregate computing and exploit self-organisation patterns to devise self-stabilising reconfiguration strategies. By simulating deployments on different kinds of complex infrastructures, we assess the flexibility of the pulverisation middleware design as well as the effectiveness and resilience of the aggregate computing-based reconfiguration policies.

Self-assembled micro-patterns in uphill-diffusion solution system.

In this work we present self-organized regular patterns in a solution system through uphill-diffusion. Micrometer thick organic semiconductor solution is sandwiched between a substrate and cover-plate. Self-assembled regular patterns can be observed on the substrate after solvent evaporation. Different micro-patterns and pattern defects were displayed and analyzed. Mechanisms of defect formation, mode selection process during patten generation, and pattern sedimentation onto substrate from solution were proposed. Organic thin film transistors were fabricated with the assembled line patterns which demonstrate a promising way to produce patterned micro/nano materials.

Collective behavior of active filaments with homogeneous and heterogeneous stiffness.

The collective dynamics of active biopolymers is crucial for many processes in life, such as cellular motility, intracellular transport, and division. Recent experiments revealed fascinating self-organized patterns of diverse active filaments, while an explicit parameter control strategy remains an open problem. Moreover, theoretical studies so far mostly dealt with active chains with uniform stiffness, which are inadequate in describing the more complicated class of polymers with varying stiffness along the backbone. Here, using Langevin dynamics simulations, we investigate the collective behavior of active chains with homogeneous and heterogeneous stiffness in a comparative manner. We map a detailed non-equilibrium phase diagram in activity and stiffness parameter space. A wide range of phase states, including melt, cluster, spiral, polar, and vortex, are demonstrated. The appropriate parameter combination for large-scale polar and vortex formation is identified. In addition, we find that stiffness heterogeneity can substantially modulate the phase behaviors of the system. It has an evident destructive effect on the long-ranged polar structure but benefits the stability of the vortex pattern. Intriguingly, we unravel a novel polar-vortex transition in both homogeneous and heterogeneous systems, which is closely related to the local alignment mechanism. Overall, we achieve new insights into how the interplay among activity, stiffness, and heterogeneity affects the collective dynamics of active filament systems.

Controlled Protein-Membrane Interactions Modulate Self-Organization of Min Protein Patterns.

Self-organizing protein patterns are crucial for living systems, governing important cellular processes such as polarization and division. While the field of protein self-organization has reached a point where basic pattern-forming mechanisms can be reconstituted in vitro using purified proteins, understanding how cells can dynamically switch and modulate these patterns, especially when transiently needed, remains an interesting frontier. Here, we demonstrate the efficient regulation of self-organizing protein patterns through the modulation of simple biophysical membrane parameters. Our investigation focuses on the impact of membrane affinity changes on Min protein patterns at lipid membranes composed of Escherichia coli lipids or minimal lipid compositions, and we present three major results. First, we observed the emergence of a diverse array of pattern phenotypes, ranging from waves over flower-shaped patterns to snowflake-like structures. Second, we demonstrated the dependency of these patterns on the density of protein-membrane linkers. Finally, we demonstrate thatthe shape of snowflake-like patterns isfine-tuned by membrane charge. Our results demonstrate the significant influence of membrane linkage as a straightforward biophysical parameter governing protein pattern formation. Our research points towards a simple yet intriguing mechanism by which cells can adeptly tune and switch protein patterns on the mesoscale.

Self-organization in spatial ecology

Biologists have long known that populations of organisms - microbes, plants, animals - can self-organize into emergent patterns. Yet, the fact that such patterns can arise with remarkable symmetry at the scale of entire ecosystems remains astonishing, even as aerial imagery has documented their existence across all continents. As the enormous scale of landscape patterns makes them experimentally intractable, ecologists have relied on theoretical modelling - typically rooted in physics - to investigate the underlying pattern-forming mechanisms. Such models have succeeded in generating mechanistic hypotheses and indicate that self-organized spatial patterns can reflect the health of an ecosystem. However, most of these hypotheses remain untested. This essay reflects on our current understanding of the causes and consequences of ecosystem-scale pattern formation.

Widespread biochemical reaction networks enable Turing patterns without imposed feedback

Understanding self-organized pattern formation is fundamental to biology. In 1952, Alan Turing proposed a pattern-enabling mechanism in reaction-diffusion systems containing chemical species later conceptualized as activators and inhibitors that are involved in feedback loops. However, identifying pattern-enabling regulatory systems with the concept of feedback loops has been a long-standing challenge. To date, very few pattern-enabling circuits have been discovered experimentally. This is in stark contrast to ubiquitous periodic patterns and symmetry in biology. In this work, we systematically study Turing patterns in 23 elementary biochemical networks without assigning any activator or inhibitor. These mass action models describe post-synthesis interactions applicable to most proteins and RNAs in multicellular organisms. Strikingly, we find ten simple reaction networks capable of generating Turing patterns. While these network models are consistent with Turing’s theory mathematically, there is no apparent connection between them and commonly used activator-feedback intuition. Instead, we identify a unifying network motif that enables Turing patterns via regulated degradation pathways with flexible diffusion rate constants of individual molecules. Our work reveals widespread biochemical systems for pattern formation, and it provides an alternative approach to tackle the challenge of identifying pattern-enabling biological systems.

Optical pattern formation of laser fields in the Rydberg atomic gases

We study the phenomena of long-wave and short-wave modulation instabilities (LMI and SMI) in Rydberg atomic gases within the framework of the nonlocal nonlinear Schrödinger equations in the local and nonlocal regions (characterized by the ratio of beam radius to radius of Rydberg blockade sphere), respectively. We further reveal the rich soliton dynamics arising from interactions of nonlinear waves triggered by LMI. We also show the variety of spatial self-organization pattern formations and their active manipulation due to SMI. Through a synthesis of theoretical analysis and numerical simulations, the self-organized optical structures reported here provide a way for realizing what we believe to be novel optical patterns and solitons based on Rydberg atomic gases.

Utilizing language models for advanced electrocardiogram analysis

Electrocardiography (ECG) signals are often referred to as the language of the heart and have been widely utilized for diagnosing various heart ailments, particularly arrhythmias. Consequently, numerous machine learning models have been employed to automatically detect heart disorders using ECG signals. In this research, the primary objective is to detect arrhythmias using a center-symmetric self-organized textual pattern. A novel feature engineering model has been introduced, which includes the following components: (i) multilevel feature extraction using the proposed center-symmetric self-organized textual pattern (CSSOTP), (ii) iterative neighborhood component analysis (INCA), and (iii) classification using k-nearest neighbors (kNN) with 10-fold cross-validation. During the feature extraction phase, a multilevel feature extraction model incorporating maximum absolute pooling (MAP) and the proposed CSSOTP was applied. The CSSOTP was designed to select the most appropriate pattern for the given data block. A large language model (LLM) was leveraged to generate text for creating patterns, and ChatGPT was used to assist in text generation. To identify the most informative features, the INCA feature selector was employed, and the selected features were subsequently classified using the kNN classifier. An impressive 96.20 % classification accuracy was achieved by the CSSOTP-based feature engineering model when tested on an ECG dataset containing 17 classes. Furthermore, comparisons with state-of-the-art feature engineering models were conducted, demonstrating that the proposed model has superior classification capabilities.

Assessing biological self-organization patterns using statistical complexity characteristics: a tool for diffusion tensor imaging analysis.

Diffusion-weighted imaging (DWI) and diffusion tensor imaging (DTI) are well-known and powerful imaging techniques for MRI. Although DTI evaluation has evolved continually in recent years, there are still struggles regarding quantitative measurements that can benefit brain areas that are consistently difficult to measure via diffusion-based methods, e.g., gray matter (GM). The present study proposes a new image processing technique based on diffusion distribution evaluation of López-Ruiz, Mancini and Calbet (LMC) complexity called diffusion complexity (DC). The OASIS-3 and TractoInferno open-science databases for healthy individuals were used, and all the codes are provided as open-source materials. The DC map showed relevant signal characterization in brain tissues and structures, achieving contrast-to-noise ratio (CNR) gains of approximately 39% and 93%, respectively, compared to those of the FA and ADC maps. In the special case of GM tissue, the DC map obtains its maximum signal level, showing the possibility of studying cortical and subcortical structures challenging for classical DTI quantitative formalism. The ability to apply the DC technique, which requires the same imaging acquisition for DTI and its potential to provide complementary information to study the brain's GM structures, can be a rich source of information for further neuroscience research and clinical practice.

The WAVE complex forms linear arrays at negative membrane curvature to instruct lamellipodia formation.

Cells generate a wide range of actin-based membrane protrusions for various cell behaviors. These protrusions are organized by different actin nucleation promoting factors. For example, N-WASP controls finger-like filopodia, whereas the WAVE complex controls sheet-like lamellipodia. These different membrane morphologies likely reflect different patterns of nucleator self-organization. N-WASP phase separation has been successfully studied through biochemical reconstitutions, but how the WAVE complex self-organizes to instruct lamellipodia is unknown. Because WAVE complex self-organization has proven refractory to cell-free studies, we leverage in vivo biochemical approaches to investigate WAVE complex organization within its native cellular context. With single molecule tracking and molecular counting, we show that the WAVE complex forms highly regular multilayered linear arrays at the plasma membrane that are reminiscent of a microtubule-like organization. Similar to the organization of microtubule protofilaments in a curved array, membrane curvature is both necessary and sufficient for formation of these WAVE complex linear arrays, though actin polymerization is not. This dependency on negative membrane curvature could explain both the templating of lamellipodia and their emergent behaviors, including barrier avoidance. Our data uncover the key biophysical properties of mesoscale WAVE complex patterning and highlight an integral relationship between NPF self-organization and cell morphogenesis.

Micropattern Fabricated by Acropetal Migration Controlled through Sequential Photo and Thermal Polymerization.

Bottom-up patterning technology plays a significant role in both nature and synthetic materials, owing to its inherent advantages such as ease of implementation, spontaneity, and noncontact attributes, etc. However, constrained by the uncontrollability of molecular movement, energy interaction, and stress, obtained micropatterns tend to exhibit an inevitable arched outline, resulting in the limitation of applicability. Herein, inspired by auxin's action mode in apical dominance, a versatile strategy is proposed for fabricating precision self-organizing micropatterns with impressive height based on polymerization-induced acropetal migration. The copolymer containing fluorocarbon chains (low surface energy) and tertiary amine (coinitiator) is designed to self-assemble on the surface of the photo-curing system. The selective exposure under a photomask establishes a photocuring boundary and the radicals would be generated on the surface, which is pivotal in generating a vertical concentration difference of monomer. Subsequent heating treatment activates the material continuously transfers from the unexposed area to the exposed area and is accompanied by the obviously vertical upward mass transfer, resulting in the manufacture of a rectilinear profile micropattern. This strategy significantly broadens the applicability of self-organizing patterns, offering the potential to mitigate the complexity and time-consuming limitations associated with top-down methods.

Active interfacial degradation/deposition of an elastic matrix by a fluid inclusion: Theory and pattern formation

During collective invasion in 3D, cohesive cellular tissues migrate within a fibrous extracellular matrix (ECM). This process requires significant remodeling of the ECM by cells, notably proteolysis at the cell–ECM interface by specialized molecules. Motivated by this problem, we develop a theoretical framework to study the dynamics of a fluid inclusion (modeling the cellular tissue) embedded in an elastic matrix (the ECM), which undergoes surface degradation/deposition. To account for the active nature of this process, we develop a continuum theory based on irreversible thermodynamics, leading to a kinetic relation for the degradation front that locally resembles the force–velocity relation of a molecular motor. We further study the effect of mechanotransduction on the stability of the cell–ECM interface, finding a variety of self-organized dynamical patterns of collective invasion. Our work identifies ECM proteolysis as an active process possibly driving the self-organization of cellular tissues.

Spatio-temporal dynamics of fairy circles in Namibia are driven by rainfall and soil infiltrability

ContextNamibia’s fairy circles (FCs) form an extraordinary vegetation pattern along the Namib Desert. Recent evidence from multiple fieldwork activities is increasingly supporting the view that FCs result from biomass-water feedbacks and plant self-organization.ObjectivesTo shed light on these biomass-water feedbacks, we focused here on a temporal analysis of the spatial FC patterns with regard to vegetation response after rainfall events.MethodsWe analyzed the distribution of FCs in 10 drone-mapped study plots of the Namib and related their spatial patterns to the soil infiltrability. Additionally, we mapped three plots repeatedly during the rainfall seasons 2020–2023 to assess how the emerging grasses within FCs changed the FC patterns after rainfall.ResultsWe found that the most regular, spatially periodic, FCs occurred in areas with deep aeolian sands where rain water infiltrates very quickly and homogenously across the study plot, which enables the most symmetric competitive interactions between the grasses. After ample rainfall following a drought period, between 58 and 34% of all mature FCs revegetated. These 1092 closing FCs were 73 times more than the 15 new FCs that formed during the same time. The closing FCs occurred in areas where there was locally a higher density of FCs, which act as underground water sources for the surrounding grasses.ConclusionsOur study shows that the dynamic vegetation response to rainfall and soil water is the key driver of the FC patterns. Overall, the research underlines that Namibia’s fairy circles are a self-organized emergent vegetation pattern that is driven by biomass-water feedbacks and the competition of grasses for limiting water resources.

Interspecific dispersal constraints suppress pattern formation in metacommunities.

Decisions to disperse from a habitat stand out among organismal behaviours as pivotal drivers of ecosystem dynamics across scales. Encounters with other species are an important component of adaptive decision-making in dispersal, resulting in widespread behaviours like tracking resources or avoiding consumers in space. Despite this, metacommunity models often treat dispersal as a function of intraspecific density alone. We show, focusing initially on three-species network motifs, that interspecific dispersal rules generally drive a transition in metacommunities from homogeneous steady states to self-organized heterogeneous spatial patterns. However, when ecologically realistic constraints reflecting adaptive behaviours are imposed-prey tracking and predator avoidance-a pronounced homogenizing effect emerges where spatial pattern formation is suppressed. We demonstrate this effect for each motif by computing master stability functions that separate the contributions of local and spatial interactions to pattern formation. We extend this result to species-rich food webs using a random matrix approach, where we find that eventually, webs become large enough to override the homogenizing effect of adaptive dispersal behaviours, leading once again to predominately pattern-forming dynamics. Our results emphasize the critical role of interspecific dispersal rules in shaping spatial patterns across landscapes, highlighting the need to incorporate adaptive behavioural constraints in efforts to link local species interactions and metacommunity structure. This article is part of the theme issue 'Diversity-dependence of dispersal: interspecific interactions determine spatial dynamics'.

The Oscillatory Behaviour of Cu-ZSM-5 Catalysts for N2O Decomposition: Investigation of Cu Species by Complementary Techniques.

Copper-exchanged ZSM-5 (Cu-ZSM-5) is a promising catalyst thanks to the Cu redox pair. A particular feature of this material consists in the presence of spontaneous isothermal oscillations which take place during N2O decomposition reaction, depending on the operating conditions. In the present work, a set of five Cu-ZSM-5 catalysts was synthesised by three procedures and three different copper precursor concentrations: i) wet impregnation, ii) single ion exchange, and iii) double ion exchange. Catalytic tests revealed that the ion-exchanged samples exhibit a low catalytic activity and no oscillatory behaviour, except for the twice-exchanged sample which achieves an average N2O conversion of 26 % at 400 °C. Conversely, the impregnated samples reach higher levels of N2O conversion (66 % for Cu5ZSM5_WI and 72 % for Cu10ZSM5_WI) and demonstrate a similar oscillating pattern. Further investigations disclosed that the most active catalysts, characterised by the presence of oscillatory behaviour, have more abundant and easily reducible copper species (ICP, EDX and H2-TPR) which interact better with the zeolitic support (FT-IR). Catalytic tests under a long time on stream (TOS) suggest that either self-organised patterns or deterministic chaos can be achieved during the reaction, depending on the operating conditions, such as temperature and contact time.